EDITED: Simpler question
Given a matroid, a coloop is an element which belongs to all bases (equivalently, to no circuit). Is there a name for the number of coloops of a matroid? Can you please give a reference?
ORIGINAL QUESTION, just for the record. We can prove that the number I was asking for is actually the number of coloops
Let $M:=\{m_1,\ldots,m_n\}$ be a finite matroid and fix one of its bases $B:=\{b_1,\ldots,b_r\}$. Then associated to $B$ there is a strict fundamental set of circuits $\{C_i\}_{i=1}^{n-r}$, so that any element of $M\setminus B$ belongs to one and only one circuit $C_i$. On the other hand, the elements of $B$ repeatedly appear in those circuits: for each $C_i$ we need some elements of $B$. But perhaps there are some elements in $B$ which are "totally independent", in the sense that they appear in no circuit at all. The "totally independent" elements of the basis are then those in $B\setminus\bigcup_i C_i$.
I think that the number of "totally independent" elements of any basis is a well defined quantity of the matroid (i.e., independent of the choice of basis). Which is the name for this quantity, and which reference can I cite?